SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 4.18 – Fundamental gain and operating modes of carrier-based SPWM.
It must be noted that the definition of the modulation index defined by Equation (4.2) (which is
reflected in Figure 4.18) could be defined differently. If the inverter was restricted to the linear
region of SPWM (no output harmonics) it would make the most sense to use the definition given
because the maximum output of the inverter would correspond to a modulation index of unity.
However, if operation in the overmodulation region is allowed (and only the fundamental
component is of interest) then the modulation index could be defined to be unity at six-step
operation by scaling it to the fundamental of the squarewave (SPWM would then correspond to
( /4) VDC
). Further, the modulation index could be defined by replacing VDC in Equation (4.1)
with VBUS (SPWM would then correspond to (1 / 2) V BUS ). Or, the peak amplitude in Equation
(4.1) could be replaced with the RMS value and either value could be described in terms of line-
line voltage instead of line-neutral voltage. Obviously there are many possible definitions for the
modulation index and a variety of these permutations are indeed found in the literature. For
example, one common choice is to use line-line RMS values referenced to VBUS; in this case, the
SPWM linear limit is given by V , , .
1 3 (1/ 2) (1/ 2) 0.6124 BUS LL RMS
Triplen Harmonic Injection
Since the PWM inverter produces output signals centered about the DC bus midpoint, the
maximum value of the terminal voltage is obviously limited to the voltage at the rail (VDC), where
the voltage drop across the switches is ignored for clarity. If harmonics cannot be tolerated (only
a fundamental component is desired) the inverter restricted to SPWM operation and the
maximum amplitude is VDC; this is called the linear SPWM limit. If harmonics are allowed the
inverter can be operated up to squarewave mode which gives a fundamental of amplitude
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